# Reducing the polynomial

• Nov 9th 2009, 02:45 AM
matt007
Reducing the polynomial
I have the following polynomial which is -x^3+5x^2-14x+16 and i am trying to reduce it, each time i try i dont get the right answer.

I have reduced it on a internet calculator and the answer comes to x^3+5x^2-2x+8 could some one show me how this answer is found.

thanks
• Nov 9th 2009, 04:30 AM
HallsofIvy
Quote:

Originally Posted by matt007
I have the following polynomial which is -x^3+5x^2-14x+16 and i am trying to reduce it, each time i try i dont get the right answer.

I have reduced it on a internet calculator and the answer comes to x^3+5x^2-2x+8 could some one show me how this answer is found.

thanks

By "reduce" you mean factor into factors having integer coefficients. The "rational root theorem" will help here. It says that any rational roots of the equation $a_nx^n+ a_{n-1}x^{n-1}+ \cdot\cdot\cdot+ a_1x+ a_0= 0$ must be of the form x= k/m where m is a factor of $a_n$ and k is a factor of $a_0$. The only factors of -1 are 1 and -1 and the only factors of 16 are 1, -1, 2, -2, 4, -4, 8, -8, 16, and -16. The means that the only possible rational roots must be 1, -1, 2, -2, 4, -4, 8, -8, 16, or -16. Put each of those into $-x^3+ 5x^2-14x+ 16$ to see if they make it 0. If none of them do then there are no rational roots and this cannot be factored with integer coefficients. If one does work, divide by (x- that root) to find the other factor.